INDIAN WELLS, Calif. — The match point does not always sum up the match, but it did on Wednesday.

Rafael Nadal, desperately trying to hold off Roger Federer, went for an old standby: a left-handed serve high to the backhand.

But the old ways no longer seem to work against this refreshed version of Federer. Where once Federer might have chipped the return and embarked on a rally, he stuck with his new game plan instead: ripping a backhand return full force.

It landed in the corner. Nadal stared at it for a moment or two, pursed his lips, raised both eyebrows (not just one) and trotted to the net, thoroughly resigned to his fate on this enchanted desert evening for Federer.

In January, in the final of the Australian Open, Federer needed to rally from a 3-1 deficit in the fifth set to win his most unexpected Grand Slam title. But in this rematch in the fourth round of the BNP Paribas Open, Federer’s 6-2, 6-3 victory required just 68 minutes as he smacked backhand winners from all sections of the court with the sort of aplomb and precision that were once too often lacking in matches against Nadal, his friendly archrival.

“In Australia, it was a very close match; I had good chances to win,” Nadal said. “Today, not. Today, he played better than me. I didn’t play my best match, and he played well. And these kind of matches, when you are not playing your best, it’s impossible to win.”

Federer’s lopsided victory was not the biggest tennis news of the day in Indian Wells. That came from the fourth-round match that preceded it, in which Nick Kyrgios, a 21-year-old Australian, defeated Novak Djokovic, the No. 2 seed, for the second time in three weeks.

Kyrgios’s 6-4, 7-6 (3) victory was a tour de force, brimming with power and precision. And there will now be a quarterfinal match on Friday between the rising Kyrgios and Federer, who still seems to be gaining altitude against the odds at age 35.

“I’m very impressed with him taking out Novak back-to-back weeks on Novak’s best surface,” Federer said.

Kyrgios explained, “I’m just in a good place mentally.”

These are words that should strike fear into the heart of all men’s tennis players.

Still just 21, Kyrgios is a frightening proposition for anyone when he is in harmony with his environment instead of fighting it. And although Kyrgios has showed his volatility many times during his short career, Djokovic, not Kyrgios, was the more unsettled and combustible man on Wednesday as the aces and winners again piled up in Kyrgios’s favor.

The result felt less like an upset if you had watched every point of Kyrgios’s quarterfinal match against Djokovic in Acapulco, Mexico, this month.

Kyrgios fired 25 aces in that 7-6 (9), 7-5 victory, which was his first match against Djokovic. Kyrgios fired 14 aces on Wednesday and did not face a single break point against the man who remains one of the very best returners in tennis, even if he is currently struggling to rediscover the same dominant form that carried him to four consecutive Grand Slam singles titles in 2015 and 2016.

Djokovic looked familiar as he finished off Juan Martín del Potro, 6-1, in the third set on Tuesday night, but he could not carry that momentum into the Kyrgios match, which he played with less than 24 hours’ rest. Djokovic declined to comment when asked about the scheduling, but he needed to play doubles later on Wednesday, which was one of the reasons he and Kyrgios were not scheduled for the night match.

“I just think there’s something not quite there,” Paul Annacone, Federer’s former coach and an analyst for Tennis Channel, said of Djokovic. “His top level is still amazing. He was great in the third set against del Potro, but there are just gaps now, and the gaps are so small: an occasional missed return he wouldn’t have missed, an occasional groundstroke four inches long instead of four inches inside the baseline. He also seems a little more dejected now when those sorts of things happen. He’s not quite as resolute.”

Wednesday’s defeat put an end to Djokovic’s 19-match winning streak in singles in Indian Wells, where he won the title in 2014, 2015 and 2016.

“The run was amazing,” Djokovic said. “I was and I am very proud of it, obviously. It had to end at some stage. Unfortunately it was today. Nick again, as he did in Acapulco a few weeks ago, he served so well, and I just wasn’t managing to get a lot of balls back on his serve.”

But there is much more to Kyrgios’s 2-0 record against Djokovic than imperious serving. There is Kyrgios’s improved two-handed backhand, a key factor in his ability to hold his own with Djokovic from the baseline. There is Kyrgios’s foot speed, versatility and tactical unpredictability.

Above all, there is his ability, at least so far this month, to avoid becoming his own worst enemy — but then nothing seems to calm Kyrgios’s inner demons quicker than facing a leading player on a show court.

He has had his misadventures: looking adrift and submissive in a loss at Wimbledon to Andy Murray last year. But he made his first major impact by upsetting Nadal in the fourth round of Wimbledon in 2014 and holds a 1-0 record against Federer after beating him in the second round in Madrid on clay in 2015, fighting off a match point.

Now, Kyrgios will face Federer on a hardcourt in Indian Wells. Federer pointed out that his loss to Kyrgios in Madrid came on his twin boys’ birthday, which he missed because he left them in Switzerland when he traveled to Spain.

“I’m happy my family is here and it’s not anybody’s birthday and I can just focus on playing tennis,” Federer said, adding, “Of course I’d like to get him back.”

Federer still has a very long way to go to settle the score with Nadal, who holds a 23-13 head-to-head advantage. But Federer has now won three straight for the first time in their 13-year rivalry, and he also holds an 11-10 edge in matches not played on clay.

That is not to diminish Nadal’s brilliance on clay, only to point out that it is a much more balanced equation in places like Indian Wells, where Federer and Nadal had split their two previous matches.

But Federer has rarely been as dominant on any surface against Nadal as he was on Wednesday, and Nadal’s resigned shake of the head after that backhand return winner on match point was entirely appropriate.

A version of this article appears in print on , on Page B14 of the New York edition with the headline: The New Normal: Federer Conquers Nadal and Djokovic Succumbs to Kyrgios. Order Reprints | Today’s Paper | Subscribe